Problems for 3505 (2011)

Size: px
Start display at page:

Download "Problems for 3505 (2011)"

Transcription

1 Problems for 505 (2011) 1. In the simplex of genotype distributions x + y + z = 1, for two alleles, the Hardy- Weinberg distributions x = p 2, y = 2pq, z = q 2 (p + q = 1) are characterized by y 2 = 4xz. Show that this set is a parabola (i.e. that there exists a line and a point such that the set is the locus of points equidistant from the point and the line), and determine the tangents at the homozygotic states. 2. Let P ij and Q ij be the frequency of gene pair (A i, A j ) among males and females, resp. Assuming discrete generations, random mating, no selective differences, etc, determine these frequencies in the next generation, and show that after two generations, Hardy Weinberg equilibrium is attained. (Maybe start with a simple example: in the parent generation, all males are A 1 A 1 and all females of type A 2 A 2 ). How do gene frequencies evolve in the selection model with w 11 > 0 and w 12 = w 22 = 0 (a dominant lethal allele)? 4. Analyze the selection model with multiplicative fitnesses: w ij = v i v j. (Assume that v 1 > v 2 > > v n.) 5. Consider the selection model with 2 alleles and fitnesses w 11 = 1, w 12 = 1 hs, and w 22 = 1 s. For s = 0.05 and the three values h = 0, 1 2, 1 (corresponding to A 1 being a dominant, intermediate, recessive allele, respectively). Using your favorite software, plot the allele frequency p 1 (t) with initial value p 1 (0) = against time t. How long does it take the allele frequency to reach p 1 (t) = 0.5 in each case? 6. Show that the selection map for 2 alleles, F : [0, 1] [0, 1], F(p) = p w 11p+w 12 (1 p) w a monotonically increasing function. (Hint: A change of variables, x = p, simplifies the calculation.) 1 p 7. Find fitness matrices W such that the selection map F has is (a) only fixed points; (b) 7 fixed points; (c) infinitely many fixed points. In all cases explain the method how you have found the matrix. 8. Show that along a continuum of fixed points in the selection map, mean fitness is constant Compute all fixed points for the selection model with W =

2 10. Which of the fixed points in the previous exercise are stable? Compute all fixed points for the selection model with W = Which of the fixed points in the previous exercise are stable? 1. Show that F t+1 p F t p 0 as t along any orbit F t p of the selection map F : n n. 14. In the selection mutation model for 2 alleles, show that p p = p(1 p) dv (p) 2V (p) dp holds with V (p) = p 2ν (1 p) 2µ w 1 ν µ. (Hint: differentiate log V ) The following 2 questions are taken from the exam Consider the selection model with n alleles A 1, A 2,...,A n in a large, randomly mating, diploid population: a) How do the frequencies p 1, p 2,...,p n evolve from one generation to the next? Explain the relevant parameters (fitness of a genotype, etc.) b) State, without proof, the fundamental theorem of natural selection. c) Show how this theorem implies that each orbit approaches the set of fixed points. d) If n =, what can be said about the number of fixed points? e) Explain how the asymptotically stable fixed points of the selection map can be found and characterized from the mean fitness function. f) Analyze the example with two alleles A, a where the fitnesses of genotypes AA, Aa, aa are given by 0.8, 1.0, 0.0, respectively. 16. In a large, randomly mating population consider a gene locus on the X-chromosome that allows for two alleles A and a. Suppose in males (that carry only one such allele) a is lethal, so that fitnesses of A and a are 1 and 0, respectively. In females, fitnesses of genotypes AA, Aa, aa are denoted as w AA, w Aa, w aa. a) Derive the equations for the change of allele frequencies in males and females. b) What happens with allele frequencies in males? c) What are the equilibrium allele frequencies, i.e., the fixed points of this map? d) For what fitness values does a polymorphic equilibrium exist? 2

3 Why does the result not depend on w aa? The following questions are taken from the exam Consider the selection model with n alleles A 1, A 2,...,A n in a large, randomly mating, diploid population: a) How do the frequencies p 1, p 2,...,p n evolve from one generation to the next? Explain the relevant parameters (fitness of a genotype, etc.) b) State, without proof, the fundamental theorem of natural selection. c) Define stability and asymptotic stability for fixed points. d) How can fixed points and asymptotically stable fixed points be characterized in terms of the mean fitness function? e) Consider three alleles A 1, A 2, A where all homozygotes are lethal (ie, w ii = 0 for i = 1, 2, ) and heterozygotes have fitnesses w 12 = 1, w 1 = w 2 = 1 : Determine all fixed points and their 4 invasion and stability properties. 18. Consider the haploid selection model in discrete time. Let A 1, A 2,...,A n be the n possible types, and p 1, p 2,...,p n be their frequencies in a large population. Let v i 0 denote the fitness of A i. a) Explain why the frequencies in the next generations are given by p i = v i p i n k=1 v kp k b) For n = 2, and v 1 = 1, v 2 =.5 find a formula for the frequencies after t generations. Determine the limit t. c) Assuming v 1 > v 2 > > v n, show that only one type survives in the long run. Which one? d) Show that mean fitness V (p) = n k=1 v kp k is monotonically increasing over time: V (p ) V (p) with equality only if p = p. e) Which p maximizes the mean fitness V (.)? 19. Consider the selection-mutation model with 2 alleles A 1, A 2 in a large, randomly mating, diploid population: a) How does the frequency p of allele A 1 evolve from one generation to the next? Explain the relevant parameters (fitness of a genotype, mutation rate, etc.) b) Show that this is equivalent to the difference equation p p = p(1 p) dv (p) 2V (p) dp with V (p) = p 2ν (1 p) 2µ w 1 ν µ, where w is mean fitness and µ, ν are mutation rates.

4 c) Is there an analogue to the fundamental theorem of natural selection for this model? Explain why each orbit converges to a fixed point. d) What can be said about the number of fixed points? e) How can the asymptotically stable fixed points of the selection-mutation map be characterized in terms of the function V? f) Consider genotypes A 1 A 1, A 1 A 2, A 2 A 2 with fitnesses given by.0,.5, 1.0, respectively, and the mutation rate from A 2 to A 1 is a small number ν (and there is no mutation in the other direction). Show that there is a unique fixed point describing selection mutation balance, and calculate it. The following questions are taken from the exam (a) Consider the model with n alleles in a large, randomly mating, diploid population. Show that the allele frequencies remain unchanged from generation to generation (the Hardy-Weinberg law). (b) Suppose that in sex-linked genes sex is determined by a pair of nonhomologous chromosomes: females XX and males XY. Consider a locus on the X chromosome with two alleles A 1 and A 2 so that female genotypes are A 1 A 1, A 1 A 2, A 2 A 2 and males genotypes are A 1, A 2. Show that genotype frequencies in females converge to Hardy-Weinberg proportions. (c) Now suppose that the model includes the selection. State, without proof, the fundamental theorem of natural selection. (d) If n =, what can be said about the number of fixed points? (e) Consider the fitness matrix W = for three alleles. Determine all fixed points and their stability properties (a) Consider the selection-mutation model with 2 alleles A 1, A 2 in a large, randomly mating, diploid population. How does the frequency p of allele A 1 evolve from one generation to the next? Explain the relevant parameters introduced in the derivation. (b) Consider the selection mutation model with 2 alleles A 1, A 2, allele frequencies p, 1 p, mutation rates µ from A 1 to A 2, and ν from A 2 to A 1. Let the function w(p) be the mean fitness function. Which role is played by the function V (p) = p 2ν (1 p) 2µ w(p) 1 µ ν in this model? (c) Consider the selection mutation model for 2 alleles, with fitnesses for A 1 A 1, A 1 A 2, A 2 A 2 given as 1 s, 1, 1, and mutation rates µ = 0, ν > 0 (i.e., only mutations to the less fit allele A 1 occur). Show that there is a unique fixed point ˆp describing selection-mutation balance, which is (approximately) given by ˆp ν. s 4

5 (d) A neutral mutant individual (genotype Aa) enters a genetically uniform (genotypes AA) population of size N 1 (N including the newcomer). Assuming random mating and non-overlapping generations, what is the probability that the mutant gene, a, will dominate the population? 22. (a) Explain the process of crossover and recombination. Consider alleles A 1, A 2,..., A n at one locus and alleles B 1, B 2,...B m at another locus, and let x ij be the frequency of gametes A i B j. If the probability for recombination between these two loci is r derive the frequencies x ij in the next generation. Show that the allele frequencies stay the same. (b) What values can r take? (c) Show that x ij converges over generations, and determine the limit. (d) Consider the model with recombination and selection. Show that in a special case of additive fitness (w ij,kl = a ik + b jl, a ik = a ki, b jl = b lj ) the average fitness function and allele frequencies in the next generation do not depend on r. Which theorem can then be used for an analysis? The following questions are taken from the exam (a) Consider a model with a selection for alleles in a large, randomly mating, diploid population. Find fitness matrices such that the selection map F has: i. only fixed points ii. infinitely many fixed points. In all cases explain the method how you have found the matrix. (b) Now suppose that the selection model also includes the mutation controlled by matrix of mutation probabilities M = (µ ij ) with special mutation rates such that µ ij = µ i, i.e. mutation rates depend only on the target gene. Derive the law describing the transformation of allele frequency p i between consequent populations p i and p i. (c) Write down the function which plays the role of mean fitness in this model. How will this function look like for the case n = 2? 24. (a) Consider the haploid selection model in discrete time. Let A 1, A 2,..., A n be the n possible types, and p 1, p 2,..., p n be their frequencies in a large population. Let v i 0 denote the fitness of A i. i. Explain why the frequencies in the next generations are given by p i = v i p i n k=1 v kp k ii. For n =, and v 1 = 1, v 2 = 0.5,v = 0.5 find a formula for the frequencies after t generations. Determine the limit t. 25. (a) State, without proof, the fundamental theorem of natural selection. 5

6 (b) Consider the fitness matrix 1 1/2 1/ W = 1/2 0 1/ 1/ 1/ 0 for three alleles. Determine all fixed points and their stability properties. (c) Define the concept of locally superior strategy for a symmetric game with n strategies and payoff matrix A. (d) Are any strategies of the game with A := W locally superior? 6

Outline of lectures 3-6

Outline of lectures 3-6 GENOME 453 J. Felsenstein Evolutionary Genetics Autumn, 007 Population genetics Outline of lectures 3-6 1. We want to know what theory says about the reproduction of genotypes in a population. This results

More information

Outline of lectures 3-6

Outline of lectures 3-6 GENOME 453 J. Felsenstein Evolutionary Genetics Autumn, 009 Population genetics Outline of lectures 3-6 1. We want to know what theory says about the reproduction of genotypes in a population. This results

More information

A. Correct! Genetically a female is XX, and has 22 pairs of autosomes.

A. Correct! Genetically a female is XX, and has 22 pairs of autosomes. MCAT Biology - Problem Drill 08: Meiosis and Genetic Variability Question No. 1 of 10 1. A human female has pairs of autosomes and her sex chromosomes are. Question #01 (A) 22, XX. (B) 23, X. (C) 23, XX.

More information

Selection Page 1 sur 11. Atlas of Genetics and Cytogenetics in Oncology and Haematology SELECTION

Selection Page 1 sur 11. Atlas of Genetics and Cytogenetics in Oncology and Haematology SELECTION Selection Page 1 sur 11 Atlas of Genetics and Cytogenetics in Oncology and Haematology SELECTION * I- Introduction II- Modeling and selective values III- Basic model IV- Equation of the recurrence of allele

More information

Natural Selection results in increase in one (or more) genotypes relative to other genotypes.

Natural Selection results in increase in one (or more) genotypes relative to other genotypes. Natural Selection results in increase in one (or more) genotypes relative to other genotypes. Fitness - The fitness of a genotype is the average per capita lifetime contribution of individuals of that

More information

Population Genetics I. Bio

Population Genetics I. Bio Population Genetics I. Bio5488-2018 Don Conrad dconrad@genetics.wustl.edu Why study population genetics? Functional Inference Demographic inference: History of mankind is written in our DNA. We can learn

More information

The Genetics of Natural Selection

The Genetics of Natural Selection The Genetics of Natural Selection Introduction So far in this course, we ve focused on describing the pattern of variation within and among populations. We ve talked about inbreeding, which causes genotype

More information

Processes of Evolution

Processes of Evolution 15 Processes of Evolution Forces of Evolution Concept 15.4 Selection Can Be Stabilizing, Directional, or Disruptive Natural selection can act on quantitative traits in three ways: Stabilizing selection

More information

8. Genetic Diversity

8. Genetic Diversity 8. Genetic Diversity Many ways to measure the diversity of a population: For any measure of diversity, we expect an estimate to be: when only one kind of object is present; low when >1 kind of objects

More information

Evolution Module. 6.2 Selection (Revised) Bob Gardner and Lev Yampolski

Evolution Module. 6.2 Selection (Revised) Bob Gardner and Lev Yampolski Evolution Module 6.2 Selection (Revised) Bob Gardner and Lev Yampolski Integrative Biology and Statistics (BIOL 1810) Fall 2007 1 FITNESS VALUES Note. We start our quantitative exploration of selection

More information

EXERCISES FOR CHAPTER 3. Exercise 3.2. Why is the random mating theorem so important?

EXERCISES FOR CHAPTER 3. Exercise 3.2. Why is the random mating theorem so important? Statistical Genetics Agronomy 65 W. E. Nyquist March 004 EXERCISES FOR CHAPTER 3 Exercise 3.. a. Define random mating. b. Discuss what random mating as defined in (a) above means in a single infinite population

More information

The Wright-Fisher Model and Genetic Drift

The Wright-Fisher Model and Genetic Drift The Wright-Fisher Model and Genetic Drift January 22, 2015 1 1 Hardy-Weinberg Equilibrium Our goal is to understand the dynamics of allele and genotype frequencies in an infinite, randomlymating population

More information

Darwinian Selection. Chapter 6 Natural Selection Basics 3/25/13. v evolution vs. natural selection? v evolution. v natural selection

Darwinian Selection. Chapter 6 Natural Selection Basics 3/25/13. v evolution vs. natural selection? v evolution. v natural selection Chapter 6 Natural Selection Basics Natural Selection Haploid Diploid, Sexual Results for a Diallelic Locus Fisher s Fundamental Theorem Darwinian Selection v evolution vs. natural selection? v evolution

More information

Microevolution Changing Allele Frequencies

Microevolution Changing Allele Frequencies Microevolution Changing Allele Frequencies Evolution Evolution is defined as a change in the inherited characteristics of biological populations over successive generations. Microevolution involves the

More information

Lecture 1 Hardy-Weinberg equilibrium and key forces affecting gene frequency

Lecture 1 Hardy-Weinberg equilibrium and key forces affecting gene frequency Lecture 1 Hardy-Weinberg equilibrium and key forces affecting gene frequency Bruce Walsh lecture notes Introduction to Quantitative Genetics SISG, Seattle 16 18 July 2018 1 Outline Genetics of complex

More information

Mechanisms of Evolution Microevolution. Key Concepts. Population Genetics

Mechanisms of Evolution Microevolution. Key Concepts. Population Genetics Mechanisms of Evolution Microevolution Population Genetics Key Concepts 23.1: Population genetics provides a foundation for studying evolution 23.2: Mutation and sexual recombination produce the variation

More information

Solutions to Even-Numbered Exercises to accompany An Introduction to Population Genetics: Theory and Applications Rasmus Nielsen Montgomery Slatkin

Solutions to Even-Numbered Exercises to accompany An Introduction to Population Genetics: Theory and Applications Rasmus Nielsen Montgomery Slatkin Solutions to Even-Numbered Exercises to accompany An Introduction to Population Genetics: Theory and Applications Rasmus Nielsen Montgomery Slatkin CHAPTER 1 1.2 The expected homozygosity, given allele

More information

Lecture 2. Basic Population and Quantitative Genetics

Lecture 2. Basic Population and Quantitative Genetics Lecture Basic Population and Quantitative Genetics Bruce Walsh. Aug 003. Nordic Summer Course Allele and Genotype Frequencies The frequency p i for allele A i is just the frequency of A i A i homozygotes

More information

URN MODELS: the Ewens Sampling Lemma

URN MODELS: the Ewens Sampling Lemma Department of Computer Science Brown University, Providence sorin@cs.brown.edu October 3, 2014 1 2 3 4 Mutation Mutation: typical values for parameters Equilibrium Probability of fixation 5 6 Ewens Sampling

More information

Outline of lectures 3-6

Outline of lectures 3-6 GENOME 453 J. Felsenstein Evolutionary Genetics Autumn, 013 Population genetics Outline of lectures 3-6 1. We ant to kno hat theory says about the reproduction of genotypes in a population. This results

More information

Segregation versus mitotic recombination APPENDIX

Segregation versus mitotic recombination APPENDIX APPENDIX Waiting time until the first successful mutation The first time lag, T 1, is the waiting time until the first successful mutant appears, creating an Aa individual within a population composed

More information

Mechanisms of Evolution

Mechanisms of Evolution Mechanisms of Evolution 36-149 The Tree of Life Christopher R. Genovese Department of Statistics 132H Baker Hall x8-7836 http://www.stat.cmu.edu/ ~ genovese/. Plan 1. Two More Generations 2. The Hardy-Weinberg

More information

STAT 536: Migration. Karin S. Dorman. October 3, Department of Statistics Iowa State University

STAT 536: Migration. Karin S. Dorman. October 3, Department of Statistics Iowa State University STAT 536: Migration Karin S. Dorman Department of Statistics Iowa State University October 3, 2006 Migration Introduction Migration is the movement of individuals between populations. Until now we have

More information

Population Genetics. with implications for Linkage Disequilibrium. Chiara Sabatti, Human Genetics 6357a Gonda

Population Genetics. with implications for Linkage Disequilibrium. Chiara Sabatti, Human Genetics 6357a Gonda 1 Population Genetics with implications for Linkage Disequilibrium Chiara Sabatti, Human Genetics 6357a Gonda csabatti@mednet.ucla.edu 2 Hardy-Weinberg Hypotheses: infinite populations; no inbreeding;

More information

Microevolution 2 mutation & migration

Microevolution 2 mutation & migration Microevolution 2 mutation & migration Assumptions of Hardy-Weinberg equilibrium 1. Mating is random 2. Population size is infinite (i.e., no genetic drift) 3. No migration 4. No mutation 5. No selection

More information

Chromosome Chr Duplica Duplic t a ion Pixley

Chromosome Chr Duplica Duplic t a ion Pixley Chromosome Duplication Pixley Figure 4-6 Molecular Biology of the Cell ( Garland Science 2008) Figure 4-72 Molecular Biology of the Cell ( Garland Science 2008) Interphase During mitosis (cell division),

More information

When one gene is wild type and the other mutant:

When one gene is wild type and the other mutant: Series 2: Cross Diagrams Linkage Analysis There are two alleles for each trait in a diploid organism In C. elegans gene symbols are ALWAYS italicized. To represent two different genes on the same chromosome:

More information

Educational Items Section

Educational Items Section Atlas of Genetics and Cytogenetics in Oncology and Haematology OPEN ACCESS JOURNAL AT INIST-CNRS Educational Items Section Hardy-Weinberg model Robert Kalmes, Jean-Loup Huret Institut de Recherche sur

More information

Introductory seminar on mathematical population genetics

Introductory seminar on mathematical population genetics Exercises Sheets Introductory seminar on mathematical population genetics WS 20/202 Kristan Schneider, Ada Akerman Ex Assume a single locus with alleles A and A 2 Denote the frequencies of the three (unordered

More information

NOTES CH 17 Evolution of. Populations

NOTES CH 17 Evolution of. Populations NOTES CH 17 Evolution of Vocabulary Fitness Genetic Drift Punctuated Equilibrium Gene flow Adaptive radiation Divergent evolution Convergent evolution Gradualism Populations 17.1 Genes & Variation Darwin

More information

Life Cycles, Meiosis and Genetic Variability24/02/2015 2:26 PM

Life Cycles, Meiosis and Genetic Variability24/02/2015 2:26 PM Life Cycles, Meiosis and Genetic Variability iclicker: 1. A chromosome just before mitosis contains two double stranded DNA molecules. 2. This replicated chromosome contains DNA from only one of your parents

More information

POPULATIONS. p t+1 = p t (1-u) + q t (v) p t+1 = p t (1-u) + (1-p t ) (v) Phenotypic Evolution: Process HOW DOES MUTATION CHANGE ALLELE FREQUENCIES?

POPULATIONS. p t+1 = p t (1-u) + q t (v) p t+1 = p t (1-u) + (1-p t ) (v) Phenotypic Evolution: Process HOW DOES MUTATION CHANGE ALLELE FREQUENCIES? Phenotypic Evolution: Process MUTATION SELECTION + POPULATIONS +/ MIGRATION DRIFT HOW DOES MUTATION CHANGE ALLELE FREQUENCIES? Assume: a single autosomal locus with 2 alleles. Frequency (A) = p Frequency

More information

Question: If mating occurs at random in the population, what will the frequencies of A 1 and A 2 be in the next generation?

Question: If mating occurs at random in the population, what will the frequencies of A 1 and A 2 be in the next generation? October 12, 2009 Bioe 109 Fall 2009 Lecture 8 Microevolution 1 - selection The Hardy-Weinberg-Castle Equilibrium - consider a single locus with two alleles A 1 and A 2. - three genotypes are thus possible:

More information

19. Genetic Drift. The biological context. There are four basic consequences of genetic drift:

19. Genetic Drift. The biological context. There are four basic consequences of genetic drift: 9. Genetic Drift Genetic drift is the alteration of gene frequencies due to sampling variation from one generation to the next. It operates to some degree in all finite populations, but can be significant

More information

The phenotype of this worm is wild type. When both genes are mutant: The phenotype of this worm is double mutant Dpy and Unc phenotype.

The phenotype of this worm is wild type. When both genes are mutant: The phenotype of this worm is double mutant Dpy and Unc phenotype. Series 1: Cross Diagrams There are two alleles for each trait in a diploid organism In C. elegans gene symbols are ALWAYS italicized. To represent two different genes on the same chromosome: When both

More information

Darwinian Selection. Chapter 7 Selection I 12/5/14. v evolution vs. natural selection? v evolution. v natural selection

Darwinian Selection. Chapter 7 Selection I 12/5/14. v evolution vs. natural selection? v evolution. v natural selection Chapter 7 Selection I Selection in Haploids Selection in Diploids Mutation-Selection Balance Darwinian Selection v evolution vs. natural selection? v evolution ² descent with modification ² change in allele

More information

Introduction to Linkage Disequilibrium

Introduction to Linkage Disequilibrium Introduction to September 10, 2014 Suppose we have two genes on a single chromosome gene A and gene B such that each gene has only two alleles Aalleles : A 1 and A 2 Balleles : B 1 and B 2 Suppose we have

More information

The Chromosomal Basis of Inheritance

The Chromosomal Basis of Inheritance The Chromosomal Basis of Inheritance Mitosis and meiosis were first described in the late 800s. The chromosome theory of inheritance states: Mendelian genes have specific loci (positions) on chromosomes.

More information

Problems on Evolutionary dynamics

Problems on Evolutionary dynamics Problems on Evolutionary dynamics Doctoral Programme in Physics José A. Cuesta Lausanne, June 10 13, 2014 Replication 1. Consider the Galton-Watson process defined by the offspring distribution p 0 =

More information

How robust are the predictions of the W-F Model?

How robust are the predictions of the W-F Model? How robust are the predictions of the W-F Model? As simplistic as the Wright-Fisher model may be, it accurately describes the behavior of many other models incorporating additional complexity. Many population

More information

4. Populationsgenetik

4. Populationsgenetik 4. Populationsgenetik Populations are never uniform, but individuals differ genetically and phenotypically. Population genetics is concerned with the study of the genetic composition of populations and

More information

Statistical Genetics I: STAT/BIOST 550 Spring Quarter, 2014

Statistical Genetics I: STAT/BIOST 550 Spring Quarter, 2014 Overview - 1 Statistical Genetics I: STAT/BIOST 550 Spring Quarter, 2014 Elizabeth Thompson University of Washington Seattle, WA, USA MWF 8:30-9:20; THO 211 Web page: www.stat.washington.edu/ thompson/stat550/

More information

Mathematical modelling of Population Genetics: Daniel Bichener

Mathematical modelling of Population Genetics: Daniel Bichener Mathematical modelling of Population Genetics: Daniel Bichener Contents 1 Introduction 3 2 Haploid Genetics 4 2.1 Allele Frequencies......................... 4 2.2 Natural Selection in Discrete Time...............

More information

Chapter 13 Meiosis and Sexual Reproduction

Chapter 13 Meiosis and Sexual Reproduction Biology 110 Sec. 11 J. Greg Doheny Chapter 13 Meiosis and Sexual Reproduction Quiz Questions: 1. What word do you use to describe a chromosome or gene allele that we inherit from our Mother? From our Father?

More information

Neutral Theory of Molecular Evolution

Neutral Theory of Molecular Evolution Neutral Theory of Molecular Evolution Kimura Nature (968) 7:64-66 King and Jukes Science (969) 64:788-798 (Non-Darwinian Evolution) Neutral Theory of Molecular Evolution Describes the source of variation

More information

UNIT 8 BIOLOGY: Meiosis and Heredity Page 148

UNIT 8 BIOLOGY: Meiosis and Heredity Page 148 UNIT 8 BIOLOGY: Meiosis and Heredity Page 148 CP: CHAPTER 6, Sections 1-6; CHAPTER 7, Sections 1-4; HN: CHAPTER 11, Section 1-5 Standard B-4: The student will demonstrate an understanding of the molecular

More information

Lesson 4: Understanding Genetics

Lesson 4: Understanding Genetics Lesson 4: Understanding Genetics 1 Terms Alleles Chromosome Co dominance Crossover Deoxyribonucleic acid DNA Dominant Genetic code Genome Genotype Heredity Heritability Heritability estimate Heterozygous

More information

Genetics and Natural Selection

Genetics and Natural Selection Genetics and Natural Selection Darwin did not have an understanding of the mechanisms of inheritance and thus did not understand how natural selection would alter the patterns of inheritance in a population.

More information

Population Genetics: a tutorial

Population Genetics: a tutorial : a tutorial Institute for Science and Technology Austria ThRaSh 2014 provides the basic mathematical foundation of evolutionary theory allows a better understanding of experiments allows the development

More information

Outline for today s lecture (Ch. 14, Part I)

Outline for today s lecture (Ch. 14, Part I) Outline for today s lecture (Ch. 14, Part I) Ploidy vs. DNA content The basis of heredity ca. 1850s Mendel s Experiments and Theory Law of Segregation Law of Independent Assortment Introduction to Probability

More information

LECTURE # How does one test whether a population is in the HW equilibrium? (i) try the following example: Genotype Observed AA 50 Aa 0 aa 50

LECTURE # How does one test whether a population is in the HW equilibrium? (i) try the following example: Genotype Observed AA 50 Aa 0 aa 50 LECTURE #10 A. The Hardy-Weinberg Equilibrium 1. From the definitions of p and q, and of p 2, 2pq, and q 2, an equilibrium is indicated (p + q) 2 = p 2 + 2pq + q 2 : if p and q remain constant, and if

More information

Reproduction and Evolution Practice Exam

Reproduction and Evolution Practice Exam Reproduction and Evolution Practice Exam Topics: Genetic concepts from the lecture notes including; o Mitosis and Meiosis, Homologous Chromosomes, Haploid vs Diploid cells Reproductive Strategies Heaviest

More information

The phenotype of this worm is wild type. When both genes are mutant: The phenotype of this worm is double mutant Dpy and Unc phenotype.

The phenotype of this worm is wild type. When both genes are mutant: The phenotype of this worm is double mutant Dpy and Unc phenotype. Series 2: Cross Diagrams - Complementation There are two alleles for each trait in a diploid organism In C. elegans gene symbols are ALWAYS italicized. To represent two different genes on the same chromosome:

More information

OPTIMALITY AND STABILITY OF SYMMETRIC EVOLUTIONARY GAMES WITH APPLICATIONS IN GENETIC SELECTION. (Communicated by Yang Kuang)

OPTIMALITY AND STABILITY OF SYMMETRIC EVOLUTIONARY GAMES WITH APPLICATIONS IN GENETIC SELECTION. (Communicated by Yang Kuang) MATHEMATICAL BIOSCIENCES doi:10.3934/mbe.2015.12.503 AND ENGINEERING Volume 12, Number 3, June 2015 pp. 503 523 OPTIMALITY AND STABILITY OF SYMMETRIC EVOLUTIONARY GAMES WITH APPLICATIONS IN GENETIC SELECTION

More information

Ch 11.4, 11.5, and 14.1 Review. Game

Ch 11.4, 11.5, and 14.1 Review. Game Ch 11.4, 11.5, and 14.1 Review Game What happens to the chromosome number during meiosis? A It doubles B It stays the same C It halves D It becomes diploid Ans: C Gametes are A Sex cells B Sperm and eggs

More information

Lecture 3. Introduction on Quantitative Genetics: I. Fisher s Variance Decomposition

Lecture 3. Introduction on Quantitative Genetics: I. Fisher s Variance Decomposition Lecture 3 Introduction on Quantitative Genetics: I Fisher s Variance Decomposition Bruce Walsh. Aug 004. Royal Veterinary and Agricultural University, Denmark Contribution of a Locus to the Phenotypic

More information

Genetical theory of natural selection

Genetical theory of natural selection Reminders Genetical theory of natural selection Chapter 12 Natural selection evolution Natural selection evolution by natural selection Natural selection can have no effect unless phenotypes differ in

More information

Name Class Date. KEY CONCEPT Gametes have half the number of chromosomes that body cells have.

Name Class Date. KEY CONCEPT Gametes have half the number of chromosomes that body cells have. Section 1: Chromosomes and Meiosis KEY CONCEPT Gametes have half the number of chromosomes that body cells have. VOCABULARY somatic cell autosome fertilization gamete sex chromosome diploid homologous

More information

The Mechanisms of Evolution

The Mechanisms of Evolution The Mechanisms of Evolution Figure.1 Darwin and the Voyage of the Beagle (Part 1) 2/8/2006 Dr. Michod Intro Biology 182 (PP 3) 4 The Mechanisms of Evolution Charles Darwin s Theory of Evolution Genetic

More information

A simple genetic model with non-equilibrium dynamics

A simple genetic model with non-equilibrium dynamics J. Math. Biol. (1998) 36: 550 556 A simple genetic model with non-equilibrium dynamics Michael Doebeli, Gerdien de Jong Zoology Institute, University of Basel, Rheinsprung 9, CH-4051 Basel, Switzerland

More information

Introduction to population genetics & evolution

Introduction to population genetics & evolution Introduction to population genetics & evolution Course Organization Exam dates: Feb 19 March 1st Has everybody registered? Did you get the email with the exam schedule Summer seminar: Hot topics in Bioinformatics

More information

Chapter 6 Linkage Disequilibrium & Gene Mapping (Recombination)

Chapter 6 Linkage Disequilibrium & Gene Mapping (Recombination) 12/5/14 Chapter 6 Linkage Disequilibrium & Gene Mapping (Recombination) Linkage Disequilibrium Genealogical Interpretation of LD Association Mapping 1 Linkage and Recombination v linkage equilibrium ²

More information

Lecture 1 Introduction to Quantitative Genetics

Lecture 1 Introduction to Quantitative Genetics Lecture Introduction to Quantitative Genetics Population Genetics Foundation Quantitative Genetics Quantitative Traits Continuous variation Varies by amount rather than kind Height, weight, IQ, etc What

More information

Mutation, Selection, Gene Flow, Genetic Drift, and Nonrandom Mating Results in Evolution

Mutation, Selection, Gene Flow, Genetic Drift, and Nonrandom Mating Results in Evolution Mutation, Selection, Gene Flow, Genetic Drift, and Nonrandom Mating Results in Evolution 15.2 Intro In biology, evolution refers specifically to changes in the genetic makeup of populations over time.

More information

Population Structure

Population Structure Ch 4: Population Subdivision Population Structure v most natural populations exist across a landscape (or seascape) that is more or less divided into areas of suitable habitat v to the extent that populations

More information

Solutions to Problem Set 4

Solutions to Problem Set 4 Question 1 Solutions to 7.014 Problem Set 4 Because you have not read much scientific literature, you decide to study the genetics of garden peas. You have two pure breeding pea strains. One that is tall

More information

UNIT V. Chapter 11 Evolution of Populations. Pre-AP Biology

UNIT V. Chapter 11 Evolution of Populations. Pre-AP Biology UNIT V Chapter 11 Evolution of Populations UNIT 4: EVOLUTION Chapter 11: The Evolution of Populations I. Genetic Variation Within Populations (11.1) A. Genetic variation in a population increases the chance

More information

(Write your name on every page. One point will be deducted for every page without your name!)

(Write your name on every page. One point will be deducted for every page without your name!) POPULATION GENETICS AND MICROEVOLUTIONARY THEORY FINAL EXAMINATION (Write your name on every page. One point will be deducted for every page without your name!) 1. Briefly define (5 points each): a) Average

More information

6.6 Meiosis and Genetic Variation. KEY CONCEPT Independent assortment and crossing over during meiosis result in genetic diversity.

6.6 Meiosis and Genetic Variation. KEY CONCEPT Independent assortment and crossing over during meiosis result in genetic diversity. 6.6 Meiosis and Genetic Variation KEY CONCEPT Independent assortment and crossing over during meiosis result in genetic diversity. 6.6 Meiosis and Genetic Variation! Sexual reproduction creates unique

More information

Meiosis -> Inheritance. How do the events of Meiosis predict patterns of heritable variation?

Meiosis -> Inheritance. How do the events of Meiosis predict patterns of heritable variation? Meiosis -> Inheritance How do the events of Meiosis predict patterns of heritable variation? Mendel s peas 1. Genes determine appearance (phenotype) 2. Genes vary and they are inherited 3. Their behavior

More information

Objectives. Announcements. Comparison of mitosis and meiosis

Objectives. Announcements. Comparison of mitosis and meiosis Announcements Colloquium sessions for which you can get credit posted on web site: Feb 20, 27 Mar 6, 13, 20 Apr 17, 24 May 15. Review study CD that came with text for lab this week (especially mitosis

More information

THEORETICAL EVOLUTIONARY GENETICS JOSEPH FELSENSTEIN

THEORETICAL EVOLUTIONARY GENETICS JOSEPH FELSENSTEIN THEORETICAL EVOLUTIONARY GENETICS JOSEPH FELSENSTEIN Theoretical Evolutionary Genetics GENOME 562 Joseph Felsenstein Department of Genome Sciences University of Washington Box 357730 Seattle, Washington

More information

List the five conditions that can disturb genetic equilibrium in a population.(10)

List the five conditions that can disturb genetic equilibrium in a population.(10) List the five conditions that can disturb genetic equilibrium in a population.(10) The five conditions are non-random mating, small population size, immigration or emigration, mutations, and natural selection.

More information

STUDY UNIT 1 MITOSIS AND MEIOSIS. Klug, Cummings & Spencer Chapter 2. Morphology of eukaryotic metaphase chromosomes. Chromatids

STUDY UNIT 1 MITOSIS AND MEIOSIS. Klug, Cummings & Spencer Chapter 2. Morphology of eukaryotic metaphase chromosomes. Chromatids STUDY UNIT 1 MITOSIS AND MEIOSIS Klug, Cummings & Spencer Chapter 2 Life depends on cell division and reproduction of organisms. Process involves transfer of genetic material. New somatic (body) cells

More information

Lecture 2. Fisher s Variance Decomposition

Lecture 2. Fisher s Variance Decomposition Lecture Fisher s Variance Decomposition Bruce Walsh. June 008. Summer Institute on Statistical Genetics, Seattle Covariances and Regressions Quantitative genetics requires measures of variation and association.

More information

- resulted in plasma membrane growth [inward] at the midpoint to divide the cells ----

- resulted in plasma membrane growth [inward] at the midpoint to divide the cells ---- Ch. 12: Genetics 1. Asexual reproduction includes - Binary fission - budding 1. Offspring of asexual reproduction - are [identical] to the original cell or organism ---- غلط] Different] - Involves inheritance

More information

AEC 550 Conservation Genetics Lecture #2 Probability, Random mating, HW Expectations, & Genetic Diversity,

AEC 550 Conservation Genetics Lecture #2 Probability, Random mating, HW Expectations, & Genetic Diversity, AEC 550 Conservation Genetics Lecture #2 Probability, Random mating, HW Expectations, & Genetic Diversity, Today: Review Probability in Populatin Genetics Review basic statistics Population Definition

More information

Module B Unit 5 Cell Growth and Reproduction. Mr. Mitcheltree

Module B Unit 5 Cell Growth and Reproduction. Mr. Mitcheltree Module B Unit 5 Cell Growth and Reproduction Mr. Mitcheltree DNA and Genetics - The Cell and Inheritance Gene = group of codons that code for a specific protein Allele = alternate form of a gene A dominant,

More information

Learning Objectives:

Learning Objectives: Review! Why is cell division important?! What are the different types of cell division?! What are these useful for?! What are the products?! What is a somatic cell?! What is a sex cell?! What is a haploid

More information

Evolutionary Genetics Midterm 2008

Evolutionary Genetics Midterm 2008 Student # Signature The Rules: (1) Before you start, make sure you ve got all six pages of the exam, and write your name legibly on each page. P1: /10 P2: /10 P3: /12 P4: /18 P5: /23 P6: /12 TOT: /85 (2)

More information

What is a sex cell? How are sex cells made? How does meiosis help explain Mendel s results?

What is a sex cell? How are sex cells made? How does meiosis help explain Mendel s results? CHAPTER 6 3 Meiosis SECTION Heredity BEFORE YOU READ After you read this section, you should be able to answer these questions: What is a sex cell? How are sex cells made? How does meiosis help explain

More information

Objective 3.01 (DNA, RNA and Protein Synthesis)

Objective 3.01 (DNA, RNA and Protein Synthesis) Objective 3.01 (DNA, RNA and Protein Synthesis) DNA Structure o Discovered by Watson and Crick o Double-stranded o Shape is a double helix (twisted ladder) o Made of chains of nucleotides: o Has four types

More information

Parts 2. Modeling chromosome segregation

Parts 2. Modeling chromosome segregation Genome 371, Autumn 2017 Quiz Section 2 Meiosis Goals: To increase your familiarity with the molecular control of meiosis, outcomes of meiosis, and the important role of crossing over in generating genetic

More information

KEY: Chapter 9 Genetics of Animal Breeding.

KEY: Chapter 9 Genetics of Animal Breeding. KEY: Chapter 9 Genetics of Animal Breeding. Answer each question using the reading assigned to you. You can access this information by clicking on the following URL: https://drive.google.com/a/meeker.k12.co.us/file/d/0b1yf08xgyhnad08xugxsnfvba28/edit?usp=sh

More information

9 Genetic diversity and adaptation Support. AQA Biology. Genetic diversity and adaptation. Specification reference. Learning objectives.

9 Genetic diversity and adaptation Support. AQA Biology. Genetic diversity and adaptation. Specification reference. Learning objectives. Genetic diversity and adaptation Specification reference 3.4.3 3.4.4 Learning objectives After completing this worksheet you should be able to: understand how meiosis produces haploid gametes know how

More information

THE OHIO JOURNAL OF SCIENCE

THE OHIO JOURNAL OF SCIENCE THE OHIO JOURNAL OF SCIENCE VOL. LV NOVEMBER, 1955 No. 6 AN OUTLINE OF THE PROCESS OF ORGANIC EVOLUTION DONALD J. BORROR Department of Zoology and Entomology, The Ohio State University, Columbus, 10 THE

More information

Population Genetics for Large Populations

Population Genetics for Large Populations Chapter 3 Population Genetics for Large Populations The diversity of life is a fundamental empirical fact of nature. Casual observation alone confirms the great variety of species. But diversity also prevails

More information

Population Genetics & Evolution

Population Genetics & Evolution The Theory of Evolution Mechanisms of Evolution Notes Pt. 4 Population Genetics & Evolution IMPORTANT TO REMEMBER: Populations, not individuals, evolve. Population = a group of individuals of the same

More information

Population genetics snippets for genepop

Population genetics snippets for genepop Population genetics snippets for genepop Peter Beerli August 0, 205 Contents 0.Basics 0.2Exact test 2 0.Fixation indices 4 0.4Isolation by Distance 5 0.5Further Reading 8 0.6References 8 0.7Disclaimer

More information

Microevolution (Ch 16) Test Bank

Microevolution (Ch 16) Test Bank Microevolution (Ch 16) Test Bank Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. Which of the following statements describes what all members

More information

Biol. 303 EXAM I 9/22/08 Name

Biol. 303 EXAM I 9/22/08 Name Biol. 303 EXAM I 9/22/08 Name -------------------------------------------------------------------------------------------------------------- This exam consists of 40 multiple choice questions worth 2.5

More information

Name Period. 3. How many rounds of DNA replication and cell division occur during meiosis?

Name Period. 3. How many rounds of DNA replication and cell division occur during meiosis? Name Period GENERAL BIOLOGY Second Semester Study Guide Chapters 3, 4, 5, 6, 11, 14, 16, 17, 18 and 19. SEXUAL REPRODUCTION AND MEIOSIS 1. What is the purpose of meiosis? 2. Distinguish between diploid

More information

Evolution PCB4674 Midterm exam2 Mar

Evolution PCB4674 Midterm exam2 Mar Evolution PCB4674 Midterm exam2 Mar 22 2005 Name: ID: For each multiple choice question select the single est answer. Answer questions 1 to 20 on your scantron sheet. Answer the remaining questions in

More information

Tutorial on Theoretical Population Genetics

Tutorial on Theoretical Population Genetics Tutorial on Theoretical Population Genetics Joe Felsenstein Department of Genome Sciences and Department of Biology University of Washington, Seattle Tutorial on Theoretical Population Genetics p.1/40

More information

How does natural selection change allele frequencies?

How does natural selection change allele frequencies? How does natural selection change allele frequencies? Alleles conferring resistance to insecticides and antibiotics have recently increased to high frequencies in many species of insects and bacteria.

More information

9-4 Meiosis Meiosis. Slide 1 of 35

9-4 Meiosis Meiosis. Slide 1 of 35 9-4 Meiosis 11-4 Meiosis 1 of 35 11-4 Meiosis Each organism must inherit a single copy of every gene from each of its parents. Gametes are formed by a process that separates the two sets of genes so that

More information

Name Period. 2. Name the 3 parts of interphase AND briefly explain what happens in each:

Name Period. 2. Name the 3 parts of interphase AND briefly explain what happens in each: Name Period GENERAL BIOLOGY Second Semester Study Guide Chapters 3, 4, 5, 6, 11, 10, 13, 14, 15, 16, and 17. SEXUAL REPRODUCTION AND MEIOSIS 1. The cell cycle consists of a growth stage and a division

More information

Chapter 17: Population Genetics and Speciation

Chapter 17: Population Genetics and Speciation Chapter 17: Population Genetics and Speciation Section 1: Genetic Variation Population Genetics: Normal Distribution: a line graph showing the general trends in a set of data of which most values are near

More information

MEIOSIS, THE BASIS OF SEXUAL REPRODUCTION

MEIOSIS, THE BASIS OF SEXUAL REPRODUCTION MEIOSIS, THE BASIS OF SEXUAL REPRODUCTION Why do kids look different from the parents? How are they similar to their parents? Why aren t brothers or sisters more alike? Meiosis A process where the number

More information

allosteric cis-acting DNA element coding strand dominant constitutive mutation coordinate regulation of genes denatured

allosteric cis-acting DNA element coding strand dominant constitutive mutation coordinate regulation of genes denatured A B C D E F G H I J K L M N O P Q R S T U V W X Y Z AA BB CC DD EE FF GG HH II JJ KK LL MM NN OO PP QQ RR SS TT UU VV allosteric cis-acting DNA element coding strand codominant constitutive mutation coordinate

More information